A layered compound such as LiCoO2 or LiNi1/3Mn1/3Co1/3O2 or a spinel compound such as LiMn2O4 has conventionally been used as a positive electrode material (positive electrode active material) for a lithium ion secondary battery. In recent years, a compound with an olivine type structure typified by LiFePO4 has attracted attention. It is known that the positive electrode material having the olivine structure is highly safe because of having high thermal stability at high temperature. A lithium ion secondary battery with LiFePO4, however, has a drawback of having a discharging/discharging voltage as low as 3.5 V and low energy density. In view of this, LiCoPO4, LiNiPO4, and the like have been suggested as phosphate-based positive electrode material that can achieve high charging/discharging voltage. However, at present, a lithium ion secondary battery with such a positive electrode material has not yet achieved sufficient capacity. Among the phosphate-based positive electrode materials, LiVOPO4 has been known as a compound that can achieve a charging/discharging voltage as high as 4 V. In such a lithium ion secondary battery with LiVOPO4, however, sufficient reversible capacity and rate characteristic have not yet been obtained. The positive electrode material as above is disclosed in Patent Documents 1 and 2 and Non-Patent Documents 1 to 5 below. The lithium ion secondary battery may be referred to as “battery” in this specification.